Is the w-coordinate of the UV coordinate system supported by Volumetric materials?
If by UV you mean unwrapped coordinates then no, volumetrics can not use UV coordinates.  This is for the exact reason you stated in your question, by unwrapping a mesh you are only assigning coordinates to the surface of your mesh, not the volume.

Here are the texture coordinates that work for volumetrics (i.e. not calculated based on the surface of the mesh).
Texture coordinate node:

Generated:  Generated coordinates are based on the bounding box of the object.  The left, bottom, front corner is (0, 0, 0) and the right, top, back corner is (1, 1, 1); the volume of the bounding box is interpolated linearly between these.  By default all procedural textures use generated coordinates.
Object: The coordinates in local-space of the specified object on the texture coordinate node.

Camera: The position in camera-space.


Other nodes:

Position (geometry node): The position in world-space.
Location (object info node): The object's position in world-space.  Note: Unlike object, camera, and position this is the position of the origin of the object possessing the material, not the point within the object.  (This one probably isn't that useful for your purposes.)

For more on texture coordinates see my explanation of texture coordinates here.